Fully 3D time-of-flight (TOF) PET scanners offer the potential for previously unachievable signal to noise ratios in clinical PET. Relatively new, fast scintillators have the combination of high speed, stopping power and light output, that make clinical TOF PET practical. Consequently it is likely that TOF will become the standard for clinical whole body PET in the near future. We will build on our experience in PET image reconstruction methodology and our recent results on rebinning of time of flight data to develop image reconstruction methods that are optimized for use with TOF-PET data. In non-TOF PET systems we have seen a progression over the past decade in the methods used for clinical studies from analytic reconstruction, to those based on Fourier rebinning and 2D iterative reconstruction, to fully 3D iterative reconstruction. The reason for this is that iterative 3D reconstruction using all of the data and more accurate models can achieve improved performance relative to the other approaches. Similarly, using the full TOF data in an iterative reconstruction framework should also lead to the best performance. The main goals of this project are: (i) to develop an optimized fully 3D TOF reconstruction method that extends our earlier MAP approach for 3D PET to TOF; and (ii) to systematically study the trade-offs involved in developing faster TOF PET reconstruction algorithms and to implement and evaluate practical methods with a computational cost consistent with their use in clinical settings. We will first develop a TOF-extension of our MAP approach to reconstruction that combines accurate physical and statistical modeling with fast convergent algorithms. Spatially variant penalty functions will be used to ensure count independent and spatially invariant resolution. We will then use this as a benchmark against which to compare other simplified methods. Among these we will investigate the use of novel Fourier rebinning methods for fast forward and backprojection of TOF-PET data, as well as data reduction methods in which we use rebinning to reduce TOF to non-TOF data. These investigations will include a study of the mathematical properties of the TOF-PET data, analysis of the bias and covariance of MAP reconstructions, and the development of fast computational algorithms. The result of this project will be a combination of practical software for TOF- PET image reconstruction with analytic studies of the properties of these methods and computational, phantom and human-study evaluation of these reconstruction methods.